Compared with the nucleon case where anomalous magnetic moments can be well described by effective field theory with the magnetic term explicitly included in the Lagrangian, the magnetic interaction between lepton and photon is incompatible with QED due to its non-renormalizability. Therefore, theoretical solutions to the discrepancy of lepton magnetic moments were proposed without exception by introducing new particles, symmetries and interactions beyond standard model [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}.
Most of the theoretical explanations focus on the muon anomalous magnetic moment and
it is somewhat challenging to find a common beyond-standard-model origin to resolve both the muon and the electron \(g-2\)  anomalies, because of their opposite signs and large magnitude difference. There have been some new physics models which attempt to explain the muon and electron \(g-2\)  simultaneously [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}.
Since the new introduced particles have nearly no visible effects to other physical observations, they are usually related to the candidates for dark matter.
